Architecture--Optimization Co-Design for Physics-Informed Neural Networks via Layer-wise Coordinate Adaptation and Gradient Conflict Resolution

arXiv:2601.12971 · cs.LG · Submitted 2026-01-19 · Read on arXiv

cs.LG

Submitted: 2026-01-19

Updated: 2026-09-13

Comments: 54 pages, 15 figures

Code: https://github.com/PanChengN/ACR-PINN

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Physical Constraints — 30× in this paper · explained in 7 episodes
• Accuracy — 28× in this paper · explained in 1 episode
• Benchmark — 12× in this paper · explained in 2 episodes
• Robustness — 12× in this paper · explained in 5 episodes
• PDE residual — 11× in this paper · explained in 2 episodes
• Attention Mechanism — 9× in this paper · explained in 2 episodes
• Representation Learning — 9× in this paper · explained in 2 episodes
• Activation Function — 7× in this paper · explained in 1 episode
• Aggregation — 7× in this paper · explained in 1 episode
• Latin Hypercube Sampling — 5× in this paper
• Consistency — 4× in this paper · explained in 3 episodes
• Fidelity — 4× in this paper · explained in 2 episodes
• Adam — 3× in this paper · explained in 2 episodes
• Adaptation — 3× in this paper · explained in 1 episode
• Alignment — 3× in this paper · explained in 1 episode
• Inverse Problem — 3× in this paper · explained in 2 episodes
• Loss Function — 3× in this paper · explained in 2 episodes
• Physics-Informed Neural Networks (PINNs) — 3× in this paper · explained in 6 episodes
• Composite Loss Function — 2× in this paper · explained in 2 episodes
• Core — 2× in this paper · explained in 2 episodes
• Dynamic Gating Mechanism — 2× in this paper · explained in 2 episodes
• Gradient Flow — 2× in this paper · explained in 2 episodes
• Multi-objective Optimization — 2× in this paper · explained in 4 episodes
• Objective Function — 2× in this paper · explained in 2 episodes
• Ablation — 1× in this paper · explained in 1 episode
• Abstraction — 1× in this paper · explained in 1 episode
• Dynamic Adaptation — 1× in this paper · explained in 2 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Failure Modes — 1× in this paper · explained in 3 episodes
• Feature Selection — 1× in this paper · explained in 4 episodes
• Layer-wise Dynamic Adaptation — 1× in this paper
• Regularization — 1× in this paper · explained in 3 episodes
• Temporal consistency — 1× in this paper · explained in 2 episodes
• Transformer — 1× in this paper · explained in 2 episodes
• Unified Framework — 1× in this paper · explained in 5 episodes

Sources

• KAN: Kolmogorov-Arnold Networks

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